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Question

*In this exercise, use properties of rational exponents to simplify the given expression. Assume that all variables represent positive numbers.*

$\left(5^{\frac{2}{3}}\right)^3$

Solution

VerifiedStep 1

1 of 2When an exponential expression is raised to a power, multiply the exponents and place the product of the exponents on the base.

So, to simplify $(5^{\frac{2}{3}})^{3}$, we will multiply $\frac{2}{3}$ and $3$ and then place it to the exponent of $5$. Therefore $(5^{\frac{2}{3}})^{3} = 5^{\frac{2}{3} \cdot 3} = 5^{2} = 25$.

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